A General Method to Create Lorenz Models
AbstractThere are currently about two dozen Lorenz models available in the literature for fitting grouped income distribution data. A general method to construct parametric Lorenz models of the weighted product form is offered in this paper. First, a general result to describe the conditions for the weighted product model to be a Lorenz curve, created by using several component parametric Lorenz models, is given. We show that the key property for an ideal component model is that the ratio between its second derivative and its first derivative is increasing. Then, a set of Lorenz models, consisting of a basic group of models along with their convex combinations, is proposed, and it is shown that any model in the set possesses this key property. Equipped with this general result and the model set, we can create a range of different weighted product Lorenz models. Finally, test results are presented which demonstrate that there may be many satisfactory models among those created. The proposed method can be generalized by finding other models with this key property.
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Bibliographic InfoPaper provided by Monash University, Department of Economics in its series Monash Economics Working Papers with number 06-09.
Length: 30 pages
Date of creation: Aug 2009
Date of revision:
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Postal: Department of Economics, Monash University, Victoria 3800, Australia
Web page: http://www.buseco.monash.edu.au/eco/
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Find related papers by JEL classification:
- D3 - Microeconomics - - Distribution
- C5 - Mathematical and Quantitative Methods - - Econometric Modeling
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-08-08 (All new papers)
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- Kwang Soo Cheong, 2002. "An empirical comparison of alternative functional forms for the Lorenz curve," Applied Economics Letters, Taylor and Francis Journals, vol. 9(3), pages 171-176.
- ZuXiang Wang & Russell Smyth, 2007. "Two New Exponential Families Of Lorenz Curves," Monash Economics Working Papers 20-07, Monash University, Department of Economics.
- Ogwang, Tomson & Rao, U. L. Gouranga, 2000. "Hybrid models of the Lorenz curve," Economics Letters, Elsevier, vol. 69(1), pages 39-44, October.
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